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Tuple

About: Tuple is a research topic. Over the lifetime, 6513 publications have been published within this topic receiving 146057 citations. The topic is also known as: tuple & ordered tuplet.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the shortest vector problem (SVP) on Euclidean lattices has been solved with less memory than enumeration, and the space requirement scales with the dimension of the lattice.
Abstract: Lattice sieving is asymptotically the fastest approach for solving the shortest vector problem (SVP) on Euclidean lattices. All known sieving algorithms for solving the SVP require space which (heuristically) grows as $2^{0.2075n+o(n)}$ , where $n$ is the lattice dimension. In high dimensions, the memory requirement becomes a limiting factor for running these algorithms, making them uncompetitive with enumeration algorithms, despite their superior asymptotic time complexity. We generalize sieving algorithms to solve SVP with less memory. We consider reductions of tuples of vectors rather than pairs of vectors as existing sieve algorithms do. For triples, we estimate that the space requirement scales as $2^{0.1887n+o(n)}$ . The naive algorithm for this triple sieve runs in time $2^{0.5661n+o(n)}$ . With appropriate filtering of pairs, we reduce the time complexity to $2^{0.4812n+o(n)}$ while keeping the same space complexity. We further analyze the effects of using larger tuples for reduction, and conjecture how this provides a continuous trade-off between the memory-intensive sieving and the asymptotically slower enumeration.

34 citations

Book ChapterDOI
22 Apr 2013
TL;DR: This paper proposes a methodology covering the most important steps of life-cycle of semantic \(\Mathcal{D}\mathcal{W}\) and a mathematical formalization of ontologies, \(\mathcal¬S}\mathCal{D})\mathcal⩽B\) and semantic \(\ MathcalµW}\, which is given.
Abstract: In last decades, semantic databases (\(\mathcal{S}\mathcal{D}\mathcal{B}\)) emerge and become operational databases, since the major vendors provide semantic supports in their products. This is mainly due to the spectacular development of ontologies in several domains like E-commerce, Engineering, Medicine, etc. Contrary to a traditional database, where its tuples are stored in a relational (table) layout, a \(\mathcal{S}\mathcal{D}\mathcal{B}\) stores independently ontology and its instances in one of the three main storage layouts (horizontal, vertical, binary). Based on this situation, \(\mathcal{S}\mathcal{D}\mathcal{B}\) become serious candidates for business intelligence projects built around the Data Warehouse (\(\mathcal{D}\mathcal{W}\)) technology. The important steps of the \(\mathcal{D}\mathcal{W}\) development life-cycle (user requirement analysis, conceptual design, logical design, ETL, physical design) are usually dealt in isolation way. This is mainly due to the complexity of each phase. Actually, the \(\mathcal{D}\mathcal{W}\) technology is quite mature for the traditional data sources. As a consequence, leveraging its steps to deal with semantic \(\mathcal{D}\mathcal{W}\) becomes a necessity. In this paper, we propose a methodology covering the most important steps of life-cycle of semantic \(\mathcal{D}\mathcal{W}\). Firstly, a mathematical formalization of ontologies, \(\mathcal{S}\mathcal{D}\mathcal{B}\) and semantic \(\mathcal{D}\mathcal{W}\) is given. User requirements are expressed on the ontological level by the means of the goal oriented paradigm. Secondly, the ETL process is expressed on the ontological level, independently of any implementation constraint. Thirdly, different deployment solutions according to the storage layouts are proposed and implemented using the data access object design patterns. Finally, a prototype validating our proposal using the Lehigh University Benchmark ontology is given.

34 citations

Proceedings ArticleDOI
18 Mar 2013
TL;DR: This work proposes two solutions to release differentially private answers for a set of sliding window aggregate queries, each consisting of query sampling and composition, and shows that they are efficient and effective.
Abstract: Regularly releasing the aggregate statistics about data streams in a privacy-preserving way not only serves valuable commercial and social purposes, but also protects the privacy of individuals. This problem has already been studied under differential privacy, but only for the case of a single continuous query that covers the entire time span, e.g., counting the number of tuples seen so far in the stream. However, most real-world applications are window-based, that is, they are interested in the statistical information about streaming data within a window, instead of the whole unbound stream. Furthermore, a Data Stream Management System (DSMS) may need to answer numerous correlated aggregated queries simultaneously, rather than a single one. To cope with these requirements, we study how to release differentially private answers for a set of sliding window aggregate queries. We propose two solutions, each consisting of query sampling and composition. We first selectively sample a subset of representative sliding window queries from the set of all the submitted ones. The representative queries are answered by adding Laplace noises in a way satisfying differential privacy. For each non-representative query, we compose its answer from the query results of those representatives. The experimental evaluation shows that our solutions are efficient and effective.

34 citations

Patent
19 Jun 2003
TL;DR: In this article, a method of estimating cardinality of a join of tables using multi-column density values and additionally using coarser density values of a subset of the multiscale density attributes is presented.
Abstract: A method of estimating cardinality of a join of tables using multi-column density values and additionally using coarser density values of a subset of the multi-column density attributes In one embodiment, the subset of attributes for the coarser densities is a prefix of the set of multi-column density attributes A number of tuples from each table that participate in the join may be estimated using densities of the subsets The cardinality of the join can be estimated using the multi-column density for each table and the estimated number of tuples that participate in the join from each table

34 citations

Journal ArticleDOI
01 Aug 1993
TL;DR: Algebraic and calculus database query languages for recursively typed complex objects based on the set and tuple constructs are studied and a technical tool, called “domain Turing machine,” is introduced and applied to characterize the expressive power of several classes of relational queries.
Abstract: Algebraic and calculus database query languages for recursively typed complex objects based on the set and tuple constructs are studied. A fundamental characteristic of such complex objects is that, in them, sets may contain members with arbitrarily deep nesting of tuple and/or set constructs. Relative to mappings from flat relations to flat relations, the algebra without while has the expressive power of the algebra on conventional complex objects with non-recursive types. The algebra plus while has the power of the computable queries. The calculus has power equivalent to the arithmetical hierarchy and also to the calculus with countable invention for conventional complex objects. A technical tool, called “domain Turing machine,” is introduced and applied to characterize the expressive power of several classes of relational queries.

34 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023203
2022459
2021210
2020285
2019306
2018266